SOLUTION: Two trains travel at right angles to each other after leaving the same train station at the same time. Two hours later they are 70.46 miles apart. If one travels 9 miles per hour s

Question 458479: Two trains travel at right angles to each other after leaving the same train station at the same time. Two hours later they are 70.46 miles apart. If one travels 9 miles per hour slower than the other, what is the rate of the faster train?
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
(2x)2+(2x+18)2=(70.46)2
4x2+4x2+72x+324=4964.6116
8x2+72x-4640.6116=0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=153683.5712 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 20.0015601544065, -29.0015601544065. Here's your graph:

Throwing out the negative answer, we get the speed of the slower train to be 20.0015601544065 mph and the speed of the faster train to be 29.0015601544065 mph..
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